Variations of Andrews-Beck type congruences

Song Heng Chan; Renrong Mao; Robert Osburn

doi:10.1016/j.jmaa.2020.124771

Variations of Andrews-Beck type congruences

Number Theory 2021-02-04 v2 Combinatorics

Authors: Song Heng Chan , Renrong Mao , Robert Osburn

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Abstract

We prove three variations of recent results due to Andrews on congruences for $NT(m,k,n)$ , the total number of parts in the partitions of $n$ with rank congruent to $m$ modulo $k$ . We also conjecture new congruences and relations for $NT(m,k,n)$ and for a related crank-type function.

Keywords

partitions rank congruences NT(m,k,n) crank-type function Andrews-Beck

Cite

@article{arxiv.2005.01272,
  title  = {Variations of Andrews-Beck type congruences},
  author = {Song Heng Chan and Renrong Mao and Robert Osburn},
  journal= {arXiv preprint arXiv:2005.01272},
  year   = {2021}
}

Comments

15 pages, typos corrected, to appear in the Journal of Mathematical Analysis and Applications

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